Due to the flexibility obtained through both materials and structures, soft robots have wide potential applications in complicated internal and external environments. This paper presents a new soft crawling robot with multiple locomotion patterns that integrate inchworm motion and various turning motions. First, the conceptual design of the proposed robot is presented by introducing thick-panel origami into the synthesis of a crawling robot, resulting in a Waterbomb-structure-inspired hybrid mechanism. Second, all locomotion patterns of the robot are precisely described and analyzed by screw theory in an algebraic manner, which include inchworm motion, restricted planar motion, quantitative turning motion, and marginal exploration motion. Then, the output motion parameter for each locomotion pattern is analytically modeled as a function of the robotic dimensional parameters, and the robot can thus be designed and controlled in a customized way for the expected output motion. Finally, the theoretical analysis and derivations are validated by simulation and physical prototype building, which lay the foundations for the design and manufacture of small-scale soft crawling robots with precise output motions in a complex planar environment.